This one will be somewhat tricky to give advice since its a school assignment and I don't know what it is that you know.
Now does the instructions indicate that you are allowed/have to to make multiple different types of buddies? Can you choose between a cat, a car, a shovel, etc? Or is it just one type? If you are to make multiple that the user can select, I'd suggest that Buddy be an interface for simplicity. If its only the one, then you can simply create a single class for Buddy.
Next, you have a class Activity. This class will contain a field for the condition change amount as well as a description of it. Set these during the constructor and allow it the accessor methods it needs. Mutators are optional.
Buddy properties will include: name, condition, and activities. Activities can be an Activity, a Collection<Activity>, or individual properties (activity1, activity2, etc). If you can't think up any other properties to give it, separate activities will fulfill the requirements of 5 properties and 3 different datatypes (string, int, activity, activity, activity), but does complicate the code when needing to check on stuff. I'd suggest a collection or array for that, and make up some other stuff. Easy if you can only create one type of buddy, you can give your cat a fur colour, a breed, eye colour, whatever. But if you can take many different types, its a bit trickier since there is no real way to enforce it (my shovel will have a brand, a type/design, a material, etc).
Come back if you run into problems with making these.
btw, right now I suggest you make a shovel buddy. Seriously. Points for creativity.